What is expand (1+e^{-t})^2 ?

The solution to expand (1+e^{-t})^2 is 1+2e^{-t}+e^{-2t}

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expand (1+e^{-t})^2

expand

(1 + e^{- t})^{2}

1 + 2 e^{- t} + e^{- 2 t}

Solution steps

(1 + e^{- t})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = 1, b = e^{- t}

= 1^{2} + 2 \cdot 1 \cdot e^{- t} + (e^{- t})^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot e^{- t} + (e^{- t})^{2} : 1 + 2 e^{- t} + e^{- 2 t}

= 1 + 2 e^{- t} + e^{- 2 t}

\frac{1}{( s + 1 ) ( s + 2 )}

(- 1 + 3 i)^{5}

(a - bi)^{2}

(1 - cos (x))^{3}

Ct an (π - x)

What is expand (1+e^{-t})^2 ?
The solution to expand (1+e^{-t})^2 is 1+2e^{-t}+e^{-2t}